Machine learning has rapidly become a powerful tool for addressing challenges in ultracold atomic systems;however,its application to intricate three-dimensional(3D)systems remains relatively underexplored.In this stud...Machine learning has rapidly become a powerful tool for addressing challenges in ultracold atomic systems;however,its application to intricate three-dimensional(3D)systems remains relatively underexplored.In this study,we introduce a3D residual network(3D Res Net)framework based on 3D convolutional neural networks(3D CNN)to predict ground states phases in 3D dipolar spinor Bose–Einstein condensates(BECs).Our results show that the 3D Res Net framework predicts ground states with high accuracy and efficiency across a broad parameter space.To enhance phase transition predictions,we incorporate data augmentation techniques,leading to a notable improvement in the model's performance.The method is further validated in more complex scenarios,particularly when transverse magnetic fields are introduced.Compared to conventional imaginary-time evolution methods(ITEM),the 3D Res Net drastically reduces computational costs,offering a rapid and scalable solution for complex 3D multi-parameter nonlinear systems.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11904309 and 12305015)the Natural Science Foundation of Hunan Province,China(Grant No.2020JJ5528)the Natural Science Foundation of Hebei Province,China(Grant No.A2024205027)。
文摘Machine learning has rapidly become a powerful tool for addressing challenges in ultracold atomic systems;however,its application to intricate three-dimensional(3D)systems remains relatively underexplored.In this study,we introduce a3D residual network(3D Res Net)framework based on 3D convolutional neural networks(3D CNN)to predict ground states phases in 3D dipolar spinor Bose–Einstein condensates(BECs).Our results show that the 3D Res Net framework predicts ground states with high accuracy and efficiency across a broad parameter space.To enhance phase transition predictions,we incorporate data augmentation techniques,leading to a notable improvement in the model's performance.The method is further validated in more complex scenarios,particularly when transverse magnetic fields are introduced.Compared to conventional imaginary-time evolution methods(ITEM),the 3D Res Net drastically reduces computational costs,offering a rapid and scalable solution for complex 3D multi-parameter nonlinear systems.
